Method for calculating a PCI margin associated with a loading pattern of a nuclear reactor, associated system, computer program and medium

ABSTRACT

A method for calculating a PCI margin associated with a loading pattern of a nuclear reactor including a core into which fuel assemblies are loaded according to the loading pattern is implemented by an electronic system. The fuel assemblies include fuel rods each including fuel pellets of nuclear fuel and a cladding surrounding the pellets. This method includes calculating a reference principal PCI margin for a reference loading pattern of the fuel assemblies in the core; calculating a reference secondary PCI margin for the reference pattern; calculating a modified secondary PCI margin for a modified loading pattern of the fuel assemblies in the core, and calculating a modified principal PCI margin for the modified pattern, depending on a comparison of the modified secondary PCI margin with the reference secondary PCI margin.

This is a continuation of U.S. application Ser. No. 16/312,280, filedDec. 20, 2018, which is a national phase of PCT/EP2017/065110, filedJun. 20, 2017, which claims priority of FR 16 01000, filed Jun. 22,2016, all of which are hereby incorporated by reference herein.

The present invention relates to a method for calculating a PCI marginassociated with a loading pattern of a nuclear reactor comprising a corein which fuel assemblies are loaded, the fuel assemblies comprising fuelrods each including nuclear fuel pellets and a cladding surrounding thepellets.

The present invention also relates to an associated electroniccalculating system, and a computer program including softwareinstructions which, when executed by a computer, implement such amethod.

The invention for example applies to light water nuclear reactors,whether using pressurized water or boiling water.

BACKGROUND

A large number of these reactors are currently used around the world.

It may be useful, in particular in countries such as France, where morethan 50% of electricity is produced using nuclear reactors, for theoverall power supplied by these reactors to vary in order to adapt tothe needs of the electrical grid that they supply.

In particular, it is desirable to be able to operate the nuclearreactors at an intermediate power during a period during which thedemand of the grid is low, typically from several days to at least 2months, before returning to the nominal power.

For all that, such an operation of a nuclear reactor, which would makeit possible to better use its capacities, must not cause a safetyproblem, in particular in case of accidental operational transients thatmay occur for example during, or shortly after, the operation atintermediate power.

SUMMARY OF THE INVENTION

One aim of the invention is to resolve this problem by providing amethod allowing to calculate a PCI margin associated with a loadingpattern of a nuclear reactor, making it possible to better exploit thecapabilities of the reactor, while retaining a safe operation.

To that end, a method is provided for calculating a PCI marginassociated with a loading pattern of a nuclear reactor comprising a corein which fuel assemblies are loaded according to the loading pattern,the fuel assemblies comprising fuel rods each including nuclear fuelpellets and a cladding surrounding the pellets, the method beingimplemented by a computer and comprising the following steps:

-   -   b) calculating a reference principal PCI margin for a reference        loading pattern of the fuel assemblies in the core,    -   c) calculating a reference secondary PCI margin for the        reference pattern,    -   d) calculating a modified secondary PCI margin for a modified        loading pattern of the fuel assemblies in the core,    -   e) calculating a modified principal PCI margin for the modified        pattern, depending on a comparison of the modified secondary PCI        margin with the reference secondary PCI margin.

The calculating method then makes it possible to calculate the value ofthe PCI margin more precisely, taking account of a variability of theloading patterns of the fuel assemblies in the core of a nuclear reactorfor a given radiation cycle, relative to a reference pattern.

The reference pattern for example defines a nominal load, also calledbreakeven load, according to which, from one radiation cycle to another,the fuel assemblies present in the core are similar, in particular interms of initial enrichment of the nuclear material, and are loaded intothe core according to a reproducible loading pattern. The referencepattern then corresponds to an operating cycle of the reactor calledbreakeven cycle.

The modified pattern makes it possible to provide flexibility relativeto the reference pattern: it for example defines a transitional load toor from the nominal load, such as a load corresponding to the startup ofa first core, a rise to the breakeven point, a change of management ofthe operation of the reactor, or to an end-of-life cycle of a reactor,or a variation relative to the reference pattern. The modified patternis also called flexibility pattern.

The modified pattern then differs from the reference pattern by at leastone fuel assembly 16 loaded into the core, some fuel assemblies 16 forexample not being loaded into the core according to the modified loadingpattern and being replaced by different fuel assemblies, for example bythe nature of the fissile material or its enrichment or the irradiationhistory of the replacement fuel assemblies.

Alternatively, the fuel assemblies 16 loaded into the core 2 areidentical between the modified pattern and the reference pattern, themodified pattern then differing from the reference pattern only by theposition of at least two fuel assemblies 16 in the core 2.

According to advantageous embodiments of the invention, the methodcomprises one or more of the following features, considered alone oraccording to any technically possible combinations:

-   -   when the modified secondary PCI margin is greater than or equal        to the reference secondary PCI margin, the modified principal        PCI margin is equal to the reference principal PCI margin; and        when the modified secondary PCI margin is less than the        reference secondary PCI margin, the modified principal PCI        margin is less than the reference principal PCI margin;    -   when the modified secondary PCI margin is less than the        reference secondary PCI margin, the modified principal PCI        margin is equal to the reference principal PCI margin reduced by        a corrective factor depending on the deviation between the        modified secondary PCI margin and the reference secondary PCI        margin;    -   the corrective factor depends on a ratio between the modified        secondary PCI margin and the reference secondary PCI margin and        is strictly between 0 and 1;    -   step b) comprises the following sub-steps:        -   b1) simulating at least one operating transient of the            nuclear reactor,        -   b2) calculating the value reached by at least one physical            quantity during the operating transient in at least part of            a cladding of a fuel rod, and        -   b3) determining, as reference principal PCI margin, the            deviation between the maximum value reached by said value            calculated in sub-step b2) during the transient and a            technological limit of the fuel rod;    -   the transient simulated in sub-step b1) is a transient chosen        from among the group consisting of: an excessive load increase,        an uncontrolled withdrawal of at least one group of control        clusters, a fall of one of the control clusters, and an        uncontrolled dilution of boric acid;    -   the method comprises, before step b), the step of: a)        determining a rupture value of the physical quantity        characterizing a rupture of the cladding;    -   step a) includes:        -   subjecting previously irradiated fuel rods to experimental            nuclear power ramps,        -   calculating the values reached by the physical quantity in            at least one cladding broken during a power ramp, and        -   selecting the rupture value as being the minimum value from            among the calculated values reached;    -   each of steps c) and d) includes, for each fuel assembly, the        following sub-steps:        -   i) simulating an evolution of the operation of the nuclear            reactor by applying, to the fuel rods, a nuclear power ramp            from the nil power,        -   ii) calculating the values reached by a physical quantity in            the claddings of the fuel rods,        -   iii) comparing the values reached to the rupture value,        -   iv) determining a power at break equal to:            -   I) the power associated with the rupture value, if a                minimum value from among the values reached calculated                in sub-step ii) is equal to the rupture value, or            -   II) infinity, if no value, from among the values reached                calculated in sub-step ii), is equal to the rupture                value,        -   v) evaluating a power margin by difference between the power            at break determined in sub-step iv) and an estimated maximum            power in the fuel assembly,        -   the corresponding secondary PCI margin, calculated during            each of steps c) and d), is equal to the minimum margin from            among the power margins evaluated for the fuel assemblies in            sub-step v);    -   neutronic calculations and thermomechanical calculations are        done to calculate each PCI margin, and the neutronic        calculations and the thermomechanical calculations are coupled        to calculate a corresponding principal PCI margin, the        thermomechanical calculations being uncoupled from the neutronic        calculations to calculate a corresponding secondary PCI margin;    -   the method further comprises the following step: f) determining        a limit value to trigger an emergency stop and/or an alarm from        the calculated principal PCI margin and for the considered        loading pattern of the fuel assemblies in the core;    -   the physical quantity is chosen from among the group consisting        of: a constraint or a constraint function in the cladding; and a        deformation energy density in the cladding;    -   the method further comprises operating the nuclear reactor by        using the calculated principal PCI margin for the considered        loading pattern of the fuel assemblies in the core.

A computer program is also provided including software instructionswhich, when executed by a computer, implement a method as defined above.

An electronic system for calculating a PCI margin associated with aloading pattern of a nuclear reactor comprising a core in which fuelassemblies are loaded according to the loading pattern is also provided,the fuel assemblies comprising fuel rods each including nuclear fuelpellets and a cladding surrounding the pellets,

the system comprising:

-   -   a first calculating module configured to calculate a reference        principal PCI margin for a reference loading pattern of the fuel        assemblies in the core,    -   a second calculating module configured to calculate, on the one        hand, a reference secondary PCI margin for the reference        pattern, and on the other hand, a modified secondary PCI margin        for a modified loading pattern of the fuel assemblies in the        core,    -   a comparison module configured to compare the modified secondary        PCI margin with the reference secondary PCI margin,

the comparison module further being configured to calculate a modifiedprincipal PCI margin for the modified pattern, depending on saidcomparison of the modified secondary PCI margin with the referencesecondary PCI margin.

BRIEF SUMMARY OF THE DRAWINGS

The invention will be better understood upon reading the followingdescription, provided solely as a non-limiting example and done inreference to the appended drawings, in which:

FIG. 1 is a schematic view of a pressurized water nuclear reactors;

FIG. 2 is a lateral schematic view of a fuel assembly of the core of thereactor of FIG. 1 ;

FIG. 3 is a longitudinal sectional schematic view of a fuel rod of theassembly of FIG. 2 ;

FIG. 4 is a block diagram of an electronic system for calculating a PCImargin associated with a loading pattern of the reactor of FIG. 1 ;

FIG. 5 is a flowchart of the method for calculating a PCI marginassociated with a loading pattern of the nuclear reactor, implemented bythe electronic system of FIG. 4 ; and

FIG. 6 is a curve illustrating the simulation of a power ramp todetermine a power at break.

DETAILED DESCRIPTION

In FIG. 1 , a pressurized water nuclear reactor 1 comprises, as is knownin itself, a core 2, a steam generator 3, a turbine 4 coupled to anelectrical energy generator 5, and a condenser 6.

The nuclear reactor 1 comprises a primary circuit 8 equipped with a pump9 and in which pressurized water circulates, along a path embodied bythe arrows in FIG. 1 . This water in particular rises through the core 2to be heated therein while providing the refrigeration of the core 2.

The primary circuit 8 further comprises a pressurizer 10 making itpossible to pressurize the water circulating in the primary circuit 8.

The water of the primary circuit 8 also supplies the steam generator 3,where it is cooled while providing the vaporization of water circulatingin a secondary circuit 12.

The steam produced by the steam generator 3 is channeled by thesecondary circuit 12 toward the turbine 4, then toward the condenser 6,where this steam is condensed by indirect heat exchange with the coolingwater circulating in the condenser 6.

The secondary circuit 12 comprises, downstream from the condenser 6, apump 13 and a heater 14.

Traditionally, the core 2 comprises fuel assemblies 16 that are loadedin a vessel 18 according to a loading pattern. A single assembly 16 isshown in FIG. 1 , but the core 2 for example comprises 157 assemblies16.

The reactor 1 comprises control clusters 20 that are positioned in thevessel 18 above certain fuel assemblies 16. A single control cluster 20is shown in FIG. 1 , but the core 2 for example comprises around sixtycontrol clusters 20.

The control clusters 20 are movable by mechanisms 22 to be inserted intothe fuel assemblies 16 that they overhang.

Traditionally, each control cluster 20 comprises rods, at least some ofwhich include a material absorbing the neutrons.

Thus, the vertical movement of each control cluster 20 makes it possibleto adjust the reactivity of the reactor 1 and allows variations of theoverall power P supplied by the core 2 from the nil power to the nominalpower PN, as a function of the pushing of the control clusters 20 intothe fuel assemblies 16.

Some of said control clusters 20 are intended to regulate the operationof the core 2, for example in terms of power or temperature, and arecalled regulating clusters. Others are intended to stop the reactor 1and are called stop clusters.

The control clusters 20 are joined into groups based on their nature andintended use. For example, for reactors of type 900 Mwe CPY, thesegroups are called G1, G2, N1, N2, R, SA, SB, SC, SD. Groups G1, G2, N1and N2, called power groups, are used overlapping for power regulation,and group R is used for temperature regulation. Groups SA, SB, SC and SDare used for the emergency stopping of the reactor 1.

As illustrated by FIG. 2 , each fuel assembly 16 traditionally comprisesan array of nuclear fuel rods 24 and a support skeleton 26 for the fuelrods 24.

The skeleton 26 traditionally comprises a lower end-piece 28, an upperend-piece 30, an array of guide tubes 31 connecting the two end-pieces28 and 30 and designed to receive the rods of the control clusters 20and to position spacer-forming grids 32 to position the arrays of fuelrods 24 and guide tubes 31.

As illustrated by FIG. 3 , each fuel rod 24 traditionally comprises acladding 33 in the form of a tube closed at its lower end by a lowerstopper 34 and at its upper end by an upper stopper 35. The fuel rod 24comprises a series of pellets 36 stacked in the cladding 33 and bearingagainst the lower stopper 34. A maintaining spring 38 is positioned inthe upper segment of the cladding 33 to bear on the upper stopper 35 andon the upper pellet 36.

Traditionally, the pellets 36 have a base of fissile material, forexample uranium oxide, and the cladding 33 is made from zirconium alloy.

In FIG. 3 , which corresponds to a fuel rod 24 derived frommanufacturing and before irradiation, radial play J exists between thepellets 36 and the cladding 33. This is illustrated more particularly bythe circled enlarged part of FIG. 3 .

When the reactor 1 is going to operate, for example at its nominal powerPN, the fuel rod 24 will be, according to the term used in the art,conditioned.

Conditioning is essentially characterized by the closing of the play Jbetween the pellets 36 and the cladding 33, due to the creep of thecladding 33 and the swelling of the pellets 36.

More specifically, the following steps are for example distinguished foreach fuel rod 24 during irradiation:

1) Under the effect of the pressure difference between the outside(water from the primary circuit 8) and the inside of the fuel rod 24,the cladding 33 gradually deforms by creeping radially toward the insideof the fuel rod 24. All other things being equal, the creep speed of thecladding 33 is one characteristic of its component material.Furthermore, the fission products, the majority of which are retained inthe pellet 36, cause swelling of the pellet 36. During this phase, thestress exerted on the cladding 33 in terms of constraints results solelyfrom the pressure differential existing between the outside and theinside of the fuel rod 24. The stresses in the cladding 33 arecompression stresses (conventionally negative).2) The contact between the pellet 36 and the cladding 33 begins after alength of time that essentially depends on local irradiation conditions(power, neutron flux, temperature, etc.) and the material of thecladding 33. In reality, the contact is established gradually over aperiod that begins with gentle contact followed by the establishment offirm contact. The increased contact pressure of the pellet 36 on theinner face of the cladding 33 leads to an inversion of the stresses inthe cladding 33, which become positive and tend to exert tensile stresson the cladding 33.3) The swelling of the pellet 36 continues, and the pellet 36 thenimposes its deformation on the cladding 33 toward the outside of thefuel rod 24. In the established steady state, this expansion is slowenough for the relaxation of the material of the cladding 33 to allow anequilibrium of the forces in the cladding 33. An analysis shows thatunder these conditions, the level of the tensile stresses is moderate(several tens of MPa) and does not present any risk with respect to theintegrity of the cladding 33.

If there is no risk of rupture of the cladding 33 in a steady state dueto the thermomechanical equilibrium in the cladding 33 at fairly lowstress levels, a risk appears once the power supplied by the fuel rod 24varies greatly.

Indeed, a power increase generates a temperature increase in the fuelrod 24. Given the difference in mechanical characteristics (thermalexpansion coefficient, Young's modulus) and the temperature differencebetween the pellet 36 of fissile material and the cladding 33 made fromzirconium alloy, the pellet 36 will expand more than the cladding 33 andimpose its deformation on the latter.

Furthermore, an operation at intermediate power lasting several daysresults in deconditioning the fuel rods 24. For the portions of the fuelrods 24 where the contact between the cladding 33 and the pellets 36 isnot established, the radial play J becomes greater. Regarding theportions of the fuel rods 24 where the play J was closed, the play J canopen again. In case of open play J, the compression creep of thecladding 33 by pressure effect resumes. This results in increasedstresses in the cladding 33 when the accidental transient occurs.

Furthermore, the presence of corrosive fission products, such as iodine,in the space between the cladding 33 and the pellet 36 creates theconditions for corrosion under stress. Thus, the deformation imposed bythe pellet 36 on the cladding 33 during a power transient, or a powervariation, can cause a rupture of the cladding 33.

Yet such a rupture of the cladding 33 is not acceptable for safetyreasons, since it may result in the release of fission products into theprimary circuit 8.

Power transients may occur during normal operation of the reactor 1,i.e., in so-called category 1 situations. Indeed, power variations maybe necessary in particular to adapt to the electrical energy needs ofthe power grid that the generator 5 supplies. Power transients may alsooccur in so-called category 2 accidental situations, such as excessivecharge increase, uncontrolled withdrawal of power control clustergroup(s) 20, boric acid dilution or undetected fall of control clusters20.

Starting from the state of the balance of the margins obtained in normaloperation, the acceptable operating duration and intermediate power isdetermined so as to guarantee the non-rupture by pellet-claddinginteraction of the claddings 33 present in the core 2 in case ofcategory 2 power transient, also called class 2 power transient.

To guarantee the integrity of the fuel rods 24 with respect to thepellet-cladding interaction, a margin is calculate with respect to therupture risk of a cladding 33 by pellet-cladding interaction (PCI) for aloading pattern of the reactor 1; this margin is called PCI margin.

Each PCI margin is a deviation relative to a characteristic quantity ofthe nuclear reactor 1 and its core 2, i.e., a delta of saidcharacteristic quantity of the nuclear reactor 1, this deviation comingfrom taking account of the rupture risk of the claddings 33 by thepellet-cladding interaction.

Each PCI margin is for example chosen from among the group consistingof: a power margin, a margin in a thermomechanical quantity associatedwith the cladding 33, a margin in an operating duration of the reactor 1at an intermediate power. The characteristic quantity of the nuclearreactor 1, a deviation, or delta, of which is determined to calculatethe PCI margin, is then the nuclear power, the thermomechanical quantityassociated with the cladding 33, or the operating duration of thereactor 1 at intermediate power.

One skilled in the art will understand that the higher the PCI marginis, the lower the likelihood of rupture of a cladding 33 is.

To that end, one for example uses an electronic system 40, in particulara computer system, for calculating a PCI margin associated with aloading pattern of the nuclear reactor 1, like that shown in FIG. 4 .

The calculating system 40 comprises a first calculating module 42configured to calculate a reference principal PCI margin for a referenceloading pattern of the fuel assemblies 16 in the core 2.

The calculating system 40 comprises a second calculating module 44configured to calculate, on the one hand, a reference secondary PCImargin for the reference loading pattern of the nuclear fuel assemblies,and on the other hand, a modified secondary PCI margin for a modifiedloading pattern of the fuel assemblies 16 in the core 2, modifiedrelative to the reference pattern.

Each principal PCI margin and each secondary PCI margin are each a PCImargin of the aforementioned type, for example a power margin, a marginon the thermomechanical quantity, a margin on the operating duration atintermediate power. The principal PCI margin and the secondary PCImargin are for example of the same type.

Alternatively, the principal PCI margin and the secondary PCI margin areeach of different types. The principal PCI margin is for example amargin on the thermomechanical quantity or a margin on the operatingduration at intermediate power. The secondary PCI margin is for examplea power margin.

One skilled in the art will understand that the secondary PCI margin isby definition the PCI margin calculated by the second calculating module44, and that the name secondary PCI margin is not in particular relatedto the secondary circuit 12, the reference principal PCI margin alsobeing calculated by the first calculating module 42.

The calculating system 40 comprises a comparison module 46 configured tocompare said modified secondary PCI margin with a reference secondaryPCI margin, the comparison module 46 further being configured tocalculate a modified principal PCI margin for the modified pattern,depending on the result of said comparison of the modified secondary PCImargin with the reference secondary PCI margin.

When said modified secondary PCI margin is less than the referencesecondary PCI margin, the comparison module 46 is configured tocalculate a value of the modified principal PCI margin that is less thanthat of the reference principal PCI margin.

Otherwise, when said modified secondary PCI margin is greater than orequal to the reference secondary PCI margin, the modified principal PCImargin is equal to the reference principal PCI margin.

This modified principal PCI margin is supplied to the operator of thenuclear reactor 1 having to carry out the modified loading pattern foradaptation, if necessary, of its operating technical specifications, inparticular the authorized operating durations at intermediate power.

The modified PCI margins, namely the modified principal PCI margin andthe modified secondary PCI margin, are also called flexibility PCImargins, said PCI margins being associated with the modified pattern,also called flexibility pattern.

As an optional addition, the calculating system 40 comprises adetermining module 48 configured to determine, from the value of thecalculated principal PCI margin corresponding to the loading pattern ofthe reactor 1, a limit value to trigger an emergency stop and/or analarm of the nuclear reactor 1, the limit value to trigger an alarmbeing reduced relative to or at most equal to the limit value to triggeran emergency stop.

In particular, when the loading pattern of the reactor 1 is the modifiedpattern, also called flexibility pattern, the limit value to trigger anemergency stop and/or an alarm of the nuclear reactor 1 is determinedfrom the value of the calculated modified principal PCI margin, and saidtriggering limit value for the flexibility pattern is then reducedrelative to, or at most equal to, the triggering limit value for thereference pattern.

In the example of FIG. 4 , the calculating system 40 comprises aninformation processing unit 50, for example made up of a memory 52 and aprocessor 54 associated with the memory 52. In this example, it furthercomprises input/output means 56 and optionally a display screen 58.

In the example of FIG. 4 , the first computing module 42, the secondcomputing module 44, the comparison module 46 and, as an optionaladdition, the determining module 48 are each made in the form ofsoftware executable by the processor 54. The memory 52 of theinformation processing unit 50 is then able to store first computingsoftware configured to compute a reference principal PCI margin for areference loading pattern, second computing software configured tocompute a reference secondary PCI margin for the reference loadingpattern and a modified secondary PCI margin for the modified loadingpattern, comparison software configured to compare the modifiedsecondary PCI margin with the reference secondary PCI margin, andfurther to compute the modified principal PCI margin based on thecomparison between the modified secondary PCI margin and the referencesecondary PCI margin. The memory 52 is, optionally and additionally,able to store determining software configured to determine a limit valuefor triggering an emergency stop and/or an alarm of the nuclear reactor1 from the calculated principal PCI margin corresponding to the loadingpattern, reference or modified depending on whether the reactor 1 isloaded. The processor 54 of the information processing unit 50 is thenable to execute the first calculating software, the second calculatingsoftware, the comparison software and, optionally and additionally, thedetermining software.

In an alternative that is not shown, the first calculating module 42,the second calculating module 44, the comparison module 46 and,optionally and additionally, the determining module 48 are each made inthe form of a programmable logic component, such as an FPGA (FieldProgrammable Gate Array), or in the form of a dedicated integratedcircuit, such as an ASIC (Applications Specific Integrated Circuit).

The first calculating module 42 is configured to calculate the referenceprincipal PCI margin for the reference loading pattern, for exampleaccording to a first methodology, for example the RPM methodology, forRenovated PCI Methodology.

The first calculating module 42 is, according to this example,configured to simulate at least one operating transient of the reactor1, calculate the value reached by a physical quantity G during theoperating transient in at least one portion of a cladding 33 of the fuelrod 24, and determine, as reference principal PCI margin, the deviationbetween the maximum value reached by said calculated value during thetransient and a technological limit of the fuel rod 24. In thismethodology, the neutron (simulation of the power transient) andthermomechanical (calculation of a physical quantity in the cladding)calculations are coupled.

The physical quantity G is for example the circumferential stress σθ orthe radial stress σ_(r) in the cladding 33. Alternatively, the physicalquantity G is a function of stress(es), for example of the differencefor instance between the circumferential stress σθ and the radial stressσ_(r). Also alternatively, the physical quantity G is the deformationenergy density DED in the cladding 33.

The transient simulated by the first calculating module 42 is preferablya transient chosen from among the group consisting of:

-   -   an excessive load increase,    -   an uncontrolled withdrawal of at least one group of control        clusters 20,    -   a fall of one of the control clusters 20, and    -   an uncontrolled boric acid dilution.

The excessive load increase corresponds to a rapid increase in the steamflow rate in the steam generator 3. Such an increase causes an imbalancebetween the thermal power of the core 2 and the load of the steamgenerator 3. This imbalance leads to cooling of the primary circuit 8.Due to the moderating and/or regulating effect of the mean temperaturein the core 2 by the control clusters 20, the reactivity, and thereforethe neutron flux, increase in the core 2. Thus, the overall power Psupplied by the core 2 increases quickly.

The uncontrolled withdrawal of groups of control clusters 20 while thereactor is operating causes an uncontrolled increase in the reactivity.This results in a rapid increase in the overall nuclear power P and theheat flux in the core 2. Until a discharge valve or pressure releasevalve of the secondary circuit 12 is opened, the extraction of heat inthe steam generator 3 increases less quickly than the power given off inthe primary circuit 8. This results in an increase of the temperatureand the pressure of the water in the primary circuit 8. To simulate thistransient, a withdrawal of the power groups is assumed at the maximumspeed of 72 pitches/min until complete removal of the control clusters20 in question.

If one or several control clusters 20 fall into the core, there is animmediate reduction in reactivity and overall power P in the core 2.Without protective action, the imbalance thus caused in the primarycircuit 8 and the secondary circuit 12 causes a drop in the entrytemperature of the water into the core 2, as well as an increase in thenuclear power by the counter-reactions, for example by Doppler effect,and the temperature regulation, until reaching a new breakeven pointbetween the primary circuit 8 and the secondary circuit 12. The presencein the core 2 of the nuclear reactor 1 of the control cluster(s) 20having fallen causes a deformation of the radial power distribution,while the removal of the regulating group leads to an axial modificationof the power.

The uncontrolled boric acid dilution leads to a decrease of the boronconcentration of the water in the primary circuit of the reactor due toa failure of a system of the reactor 1. It causes an insertion ofreactivity, which leads to a local increase of the linear power in thecore 2.

The technological limit of a fuel rod 24 is established from valuesreached by the physical quantity in claddings during experimental powerramps, done in test reactors, on fuel rod segments representative offuel rods 24 and previously irradiated in a nuclear power reactor andhaving different combustion rates. The technological limit of thephysical quantity corresponds to the minimum value of the physicalquantity from among the values reached during experimental tests. Belowthis limit, no fuel rod 24 rupture by pellet-cladding interaction isconsidered. Above it, the likelihood of a cladding rupture bypellet-cladding interaction is not nil.

The second calculating module 44 is configured to calculate eachsecondary PCI margin, for example using a second methodology differentfrom the first methodology, for example the methodology called power atbreak methodology.

The second calculating module 44 is, according to this example, for eachfuel assembly 16, configured to simulate an evolution of the operationof the nuclear reactor 1 by applying, to each fuel rod 24, a nuclearpower ramp from the nil power, in order to calculate the values reachedby a physical quantity locally in each cladding 33 of each fuel rod 24present in the core 2 and to determine, if applicable, a local power atbreak equal to the power associated with the local power of the physicalquantity when this value reaches the technological limit. If thetechnological limit is not reached, the local power at break at theconsidered point is infinite. In this methodology, the simulated powerramp is a theoretical ramp, independent of the neutronic studies, andthe thermomechanical calculations are then uncoupled from the neutroniccalculations.

The second calculating module 44 is further configured to evaluate, ateach point of the core 2, a power margin by difference between the powerat break calculated for a loading pattern and a local maximum powerestimated at the same moment of the irradiation cycle for the consideredloading pattern, the secondary PCI margin calculated according to thesecond methodology then depending on the minimum margin from among thepower margins thus evaluated. The calculated secondary PCI margin is forexample equal to the minimum margin from among said evaluated powermargins.

The estimated maximum power is for example a power envelope at any pointof the core 2 and taking account of all of the limiting transients. Thisestimated maximum power in particular takes into account powertransients that may occur in so-called category 2 accidental situations.

One skilled in the art will then understand that, in the exampledescribed above, the first calculating module 42 is more generallyconfigured to calculate a principal PCI margin according to the firstmethodology, called renovated PCI methodology, and that the secondcalculating module 44 is more generally configured to calculate asecondary PCI margin, reference or modified, according to the secondmethodology, called power at break methodology.

The comparison module 46 is then configured to compare the modifiedsecondary PCI margin with said reference secondary PCI margin, and todeduce the modified principal PCI margin therefrom.

When the modified secondary PCI margin is greater than or equal to thereference secondary PCI margin, the comparison module 46 is thenconfigured to validate, as modified principal PCI margin, associatedwith the modified loading pattern, the value of the reference principalPCI margin.

When the modified secondary PCI margin is less than the referencesecondary PCI margin, the comparison module 46 is configured tocalculate a value of the modified principal PCI margin that is less thanthat of the reference principal PCI margin. The modified principal PCImargin is, for example, calculated by applying a corrective factor tothe reference principal PCI margin. The corrective factor is for examplea positive value subtracted from the reference principal PCI margin, ora multiplicative factor strictly between 0 and 1.

The corrective factor preferably depends on the deviation between themodified secondary PCI margin and the reference secondary PCI margin.The corrective factor for example depends on a ratio between themodified secondary PCI margin and the reference secondary PCI margin.The modified principal PCI margin is then for example calculated bymultiplying the reference principal PCI margin by the modified secondaryPCI margin and the reference secondary PCI margin.

The modified principal PCI margin is sent to the operator needing tocarry out said modified loading pattern in order to adapt, if needed,the protection thresholds of his reactor 1 that are unchanged, theoperating duration at intermediate power during the radiation cycle, andtherefore to best exploit the capacities of the reactor 1 while reducingthe risks of damage to the fuel rods 24.

Optionally and additionally, the determining module 48 is configured todetermine the limit value for triggering of an emergency stop and/or analarm from the calculated principal PCI margin and according to theconsidered loading pattern, the reference principal PCI pattern beingused when the loading pattern is the reference loading pattern, and themodified principal PCI pattern being used when the loading pattern isthe modified loading pattern. In other words, the determining module 48is configured to determine emergency stop and/or alarm thresholds as afunction of the calculated principal PCI margin, and more generally touse the calculated principal PCI margin in order to control the reactor1.

The method for calculating a PCI margin associated with a loadingpattern is illustrated by the flowchart of FIG. 5 .

During a first step 100, a reference principal PCI margin is calculatedby the first calculating module 42 for the reference loading pattern ofthe fuel assemblies 16 in the core 2.

The reference principal PCI margin is preferably calculated using theRPM methodology, as previously described. One skilled in the art willnote that document FR 2 846 139 A1, in particular in pages 9 to 19, inlight of FIGS. 5 to 11, also relates to the RPM methodology.

The pellet-cladding interaction being local by nature, the risk ofcladding rupture is determined from the thermomechanical state of thefuel rods 24 in each mesh of the core 2 of the nuclear reactor 1. Thethermomechanical state of a fuel rod 24 at a given moment depends on thepower histories experienced by said fuel rod 24 from its first insertionin new condition into the core 2 up to the moment of the calculation.

To calculate the reference principal PCI margin, the first calculatingmodule 42 begins, for example, by determining a value of a physicalquantity G for each axial mesh of each fuel rod 24 present in the core 2of the reactor 1.

The power histories are created by the first calculating module 42 foreach fuel rod 24 present in the core 2, for example by finite elementmodeling of the neutronic behavior of the fuel rods 24.

The operating histories relative to each fuel rod 24 are generated fordifferent operating modes of the core 2, namely:

-   -   the basic operation, where the overall power P of the core 2 is        equal to its nominal power PN,    -   the operation at intermediate power with the control clusters 20        inserted into the fuel assemblies 16,    -   the operation at intermediate power with the control clusters 20        removed from the fuel assemblies 16.

The histories can be generated taking account of different intermediatepower levels, for example 10% PN, 30% PN, 50% PN, etc.

The first calculating module 42 next simulates at least one operatingtransient of the nuclear reactor 1, such as one or several accidentaloperating transients of the reactor 1 that cause abrupt powervariations. The accidental transients are for example simulated fromsimulated initial conditions corresponding to a so-called category 1situation, at several moments in each cycle.

The simulated transients are the so-called category 2 accidentaltransients causing the strongest and fastest power variations in thecore 2, such as the transients previously described, namely theexcessive load increase, the uncontrolled withdrawal of groups ofcontrol clusters 20, while the reactor 1 is powered on, and fallingcluster(s) 20.

The first calculating module 42 then calculates the maximum valuereached by the physical quantity G, such as the circumferential stressσθ, during the operating transient in each axial mesh of each fuel rod24, then compares, for each axial mesh, said maximum value to saidtechnological limit and determines the PCI margin as being thedifference between the technological limit and the maximum value of thephysical quantity on the core 2.

During a second step 110, the reference secondary PCI margin iscalculated by the second calculating module 44 for the reference loadingpattern of the fuel assemblies 16 in the core 2.

The reference secondary PCI margin is preferably calculated using thesecond methodology, called power at break methodology.

The second calculating module 44 then simulates, for each fuel assembly16, an evolution of the operation of the nuclear reactor 1 by applying,to each axial mesh of each fuel rod 24, after a plateau 112 withsubstantially constant power, a power ramp 114 from the nil power, asshown in FIG. 6 . The second calculating module 44 then calculates thevalues reached locally in each axial mesh of each fuel rod 24, by aphysical quantity and, if the technological limit is exceeded,determines a power at break P_(lin_rupt) equal to the power associatedwith the physical quantity at break. In the example of FIG. 6 , thepower ramp 114 is a linear power ramp, and the physical quantity is thedeformation energy density DED in the cladding 33, the power at breakP_(lin_rupt) then corresponding to the maximum deformation energydensity DED_(MAX), i.e., to the value of the deformation energy densityreached when the cladding 33 ruptures.

The second calculating module 44 next evaluates, for reached each axialmesh of each fuel rod 24, a power margin by difference between the powerat break and the maximum power over all of the transients, thecalculated secondary PCI margin according to the second methodology thendepending on the minimum margin from among the power margins evaluatedfor each axial mesh of each fuel rod 24 of each fuel assembly 16.

During the following step 120, the second calculating module 44calculates the modified secondary PCI margin for the modified loadingpattern of the fuel assemblies 16 in the core 2.

The modified loading pattern for example differs from the referenceloading pattern by at least one fuel assembly loaded into the core.

Alternatively, the fuel assemblies 16 loaded into the core are identicalbetween the modified loading pattern and the reference loading pattern,the modified pattern then differing from the reference pattern by theposition of at least two fuel assemblies in the core 2.

The modified secondary PCI margin is preferably calculated using thesecond methodology, called power at break methodology, i.e., asindicated previously for step 110, but with the modified loadingpattern.

During the following step 130, the comparison module 46 then comparessaid modified secondary PCI margin with said reference secondary PCImargin, and validates, as modified principal PCI margin, the referenceprincipal PCI margin previously calculated, when said modified secondaryPCI margin is greater than or equal to said reference secondary PCImargin.

When said modified secondary PCI margin is less than said referencesecondary PCI margin, the comparison module 46 calculates the modifiedprincipal PCI margin, the latter then having a value lower than that ofthe reference principal PCI margin previously calculated, for example byapplying a corrective factor to said reference principal PCI margin. Thecorrective factor is for example a positive value subtracted from thereference principal PCI margin, or a multiplicative factor strictlybetween 0 and 1.

The corrective factor preferably depends on the deviation between themodified secondary PCI margin and the reference secondary PCI margin.The corrective factor for example depends on a ratio between themodified secondary PCI margin and the reference secondary PCI margin.The modified principal PCI margin is then for example obtained bymultiplying the reference principal PCI margin by the modified secondaryPCI margin and the reference secondary PCI margin.

This principal PCI margin value, in particular the modified principalPCI margin when the reactor 1 is loaded according to the modifiedpattern, is supplied to the operator of the nuclear reactor 1 having tocarry out the modified loading pattern for adaptation, if necessary, ofits operating technical specifications.

Optionally and additionally, from this value of the modified principalPCI margin, associated with the modified loading pattern, thedetermining module 48 then establishes emergency stop and/or alarmthresholds, and more generally uses the modified principal PCI margin toreduce, if applicable, the emergency stop and/or alarm thresholds tocontrol the reactor 1.

Thus, the calculating method and the calculating system 40 according tothe present disclosure make it possible to calculate a PCI margin,taking to account a variability of the loading patterns, considering forexample a transitional load to or from the nominal load, such as a loadcorresponding to the startup of a first core, a rise to the breakevenpoint, a change of management of the operation of the reactor, or to anend-of-life cycle of a reactor, or a variation relative to the referencepattern.

The calculating method and the calculating system 40 according to thepresent disclosure also make it possible to adjust, if applicable, thesettings for certain stoppage or alarm thresholds of the nuclear reactor1 to lower values if necessary and to convert the deviationcorresponding to the PCI margin to an authorized operating duration atintermediate power. It is thus possible to provide safe operation of thenuclear reactor 1, while best exploiting its capacities, in particularin case of prolonged operation at intermediate power (POIP).

The calculating method and the calculating system 40 according to thepresent disclosure thus allow a better match between fuel management andthe maneuverability of the reactor 1 for the operator: choice of loadingpattern, justification for transition cycles, possibility of extendingPOIP durations.

What is claimed is:
 1. A method for calculating a pellet-claddinginteraction margin associated with a loading pattern of a nuclearreactor comprising a core in which fuel assemblies are loaded accordingto the loading pattern, the fuel assemblies comprising fuel rods eachincluding nuclear fuel pellets and a cladding surrounding the pellets,the method being implemented by a computer and comprising the followingsteps: b) calculating a reference principal pellet-cladding interactionmargin for a reference loading pattern of the fuel assemblies in thecore, c) calculating a reference secondary pellet-cladding interactionmargin for the reference loading pattern, d) calculating a modifiedsecondary pellet-cladding interaction margin for a modified loadingpattern of the fuel assemblies in the core, e) calculating a modifiedprincipal pellet-cladding interaction margin for the modified loadingpattern, depending on a comparison of the modified secondarypellet-cladding interaction margin with the reference secondarypellet-cladding interaction margin; the method further comprisingcontrolling, by the computer, the state of the power balance of thenuclear reactor by using the calculated principal pellet-claddinginteraction margin for a considered loading pattern of the fuelassemblies in the core to avoid rupture by pellet-cladding interactionof the claddings present in the core, wherein when the modifiedsecondary pellet-cladding interaction margin is greater than or equal tothe reference secondary pellet-cladding interaction margin, the modifiedprincipal pellet-cladding interaction margin is equal to the referenceprincipal pellet-cladding interaction margin, and when the modifiedsecondary pellet-cladding interaction margin is less than the referencesecondary pellet-cladding interaction margin, the modified principalpellet-cladding interaction margin is less than the reference principalpellet-cladding interaction margin.
 2. The method according to claim 1,wherein, when the modified secondary pellet-cladding interaction marginis less than the reference secondary pellet-cladding interaction margin,the modified principal pellet-cladding interaction margin is equal tothe reference principal pellet-cladding interaction margin reduced by acorrective factor depending on the deviation between the modifiedsecondary pellet-cladding interaction margin and the reference secondarypellet-cladding interaction margin.
 3. The method according to claim 2,wherein the corrective factor depends on a ratio between the modifiedsecondary pellet-cladding interaction margin and the reference secondarypellet-cladding interaction margin and is strictly between 0 and
 1. 4.The method according to claim 1, wherein step b) comprises the followingsub-steps: b1) simulating at least one operating transient of thenuclear reactor, b2) calculating the value reached by at least onephysical quantity during the operating transient in at least part of acladding of a fuel rod, and b3) determining, as reference principalpellet-cladding interaction margin, the deviation between the maximumvalue reached by the value calculated in sub-step b2) during thetransient and a technological limit of the fuel rod.
 5. The methodaccording to claim 4, wherein the transient simulated in sub-step b1) isa transient chosen from among the group consisting of: an excessive loadincrease, an uncontrolled withdrawal of at least one group of controlclusters, a fall of one of the control clusters, and an uncontrolledboric acid dilution.
 6. The method according to claim 4, wherein themethod comprises, before step b), the following step: a) determining arupture value of the physical quantity characterizing a rupture of thecladding.
 7. The method according to claim 6, wherein step a) includes:subjecting previously irradiated fuel rods to experimental nuclear powerramps, calculating the values reached by the physical quantity in atleast one cladding broken during a power ramp, and selecting the rupturevalue as being the minimum value from among the calculated valuesreached.
 8. The method according to claim 1, wherein the method furthercomprises the following step: f) determining a limit value to trigger anemergency stop and/or an alarm from the calculated principalpellet-cladding interaction margin and for the considered loadingpattern of the fuel assemblies in the core.
 9. The method according toclaim 4, wherein the physical quantity is chosen from among the groupconsisting of: a constraint or a constraint function in the cladding;and a deformation energy density in the cladding.
 10. A non-transitorycomputer-readable medium including a computer program comprisingsoftware instructions which, when executed by a computer, carry out themethod according to claim
 1. 11. An electronic system for calculating apellet-cladding interaction margin associated with a loading pattern ofa nuclear reactor comprising a core in which fuel assemblies are loadedaccording to the loading pattern, the fuel assemblies comprising fuelrods each including nuclear fuel pellets and a cladding surrounding thepellets, the electronic system comprising: a first calculating moduleconfigured to calculate a reference principal pellet-claddinginteraction margin for a reference loading pattern of the fuelassemblies in the core; a second calculating module configured tocalculate, on the one hand, a reference secondary pellet-claddinginteraction margin for the reference loading pattern, and on the otherhand, a modified secondary margin for a modified loading pattern of thefuel assemblies in the core; and a comparison module configured tocompare the modified secondary pellet-cladding interaction margin withthe reference secondary pellet-cladding interaction margin, thecomparison module further being configured to calculate a modifiedprincipal pellet-cladding interaction margin for the modified loadingpattern, depending on the comparison of the modified secondarypellet-cladding interaction margin with the reference secondarypellet-cladding interaction margin, wherein when the modified secondarypellet-cladding interaction margin is greater than or equal to thereference secondary pellet-cladding interaction margin, the modifiedprincipal pellet-cladding interaction margin is equal to the referenceprincipal pellet-cladding interaction margin, and when the modifiedsecondary pellet-cladding interaction margin is less than the referencesecondary pellet-cladding interaction margin, the modified principalpellet-cladding interaction margin is less than the reference principalpellet-cladding interaction margin.